Leaf-cutting ants form some of the largest social insect colonies in the world, with some consisting of as many as 8 million workers.

"Honey bee hives will divide and swarm when they hit about 40,000 workers," says Burd, an evolutionary ecologist.

"Those are just little towns compared to what these leaf-cutting ants are doing."

The insects cut up leaves to feed a fungus in the nest, which in turn is eaten by growing larvae.

The leaves are carried over large distances along tracks they create on the forest floor, which can run up to 150 or 200 metres.

"Much in the way any city would bring resources in from the countryside to the city where industries transform these into other products," says Burd.

He says the roads constructed by leaf-cutting ants are analogous to the roads of a city.

Limits to growth

Burd and Bruce were interested in studying the relationship between the size of an ant colony and its rate of leaf collection.

They studied 18 colonies of leaf-cutting ants in Central America and found that as the colony gets bigger the foraging activity per worker decreased.

"As they travel further and further from the centre in order to retrieve resources they become less efficient at it," says Burd.

Burd and Bruce found that individual ants work at roughly the same rate as the colony gets bigger, but the distance they have to carry the leaves means it takes them longer to deliver the same amount of leaf material to the nest.

The deployment of a greater number of foragers as the colony got larger did not overcome the disadvantage of the extra travel time.

"Obviously there's a limit at which it is more costly to try to retrieve the resources than the resources are worth when you bring them back," says Burd.

"There is therefore a limit to the size of the territory that any one colony can exploit."

Scaling

A similar "scaling" relationship has been found in previous studies that showed the metabolic rate of an ant colony (rate of CO2 production) decreased as it got bigger.

The scaling relationship has also been found in other areas of biology and ecology.

For example, it's been suggested that the metabolic rate of an organism is limited by the vascular systems that feeds cells with nutrients.

As an organism grows, the vascular system changes in a way that slows down metabolism - explaining why an elephant may eat more than a mouse, but it eats less and has slower metabolism per unit of body mass

And previous research suggests similar principles also apply to human societies.

"If a city doubles in size it doesn't double the number of roads," says Burd.

Burd says the latest findings could help understand limits to the growth of a city, which also depends on the transport of materials.